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For nonlinear stochastic systems, controlling low‐order moment indexes, such as mean and variance, may not effectively achieve actual control requirements since they do not reflect the complete statistical characteristics of random variables. Instead, the probability density function (PDF), which provides complete characterization of statistical properties, can be used to control each order moment...
Aiming at a class of nonlinear stochastic systems with additive Gaussian White noise and the polynomial nonlinear function we propose a shape control technique for probability density function (PDF) of the state variable. Controlling the PDF shape requires to design a controller making the PDF shape as close as possible to the desired PDF, and this actually is to determine the parameters of the controller...
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